Current Situation and Thinking on the Thinking Problems in the Elementary Mathematics Textbooks——Taking the Textbooks Published by Southwest Normal University Press as an Example
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In the elementary mathematics textbooks published by Southwest Normal University Press,the proportion of the number of thinking problem is high in the knowledge field of number and algebra,while low in the field of statistics and probability;the proportion of thinking problem in which the situation is based on mathematics is high,while the proportion based on cartoon and others is low;the number of thinking problem balances on some aspects such as knowledge characteristics,thinking level and open-ended in all grades;the proportion of thinking problem which has embedded questions is low on self-explanation;most of them provide some space to explore for students,reflecting higher order thinking.Suggestions on thinking problems writing are as followed: studying the spirit of mathematics curriculum standard on thinking problems writing deeply;making overall arrangement in the full set of textbooks;paying attention to pupils' reading level;adding some tips properly in some difficult thinking problems;adding some embedded questions properly in the end of some thinking problems.Keywords:
Higher-Order Thinking
Thinking processes
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The traditional teaching of mathematics neglects the development of students' thinking,due to the constraints of examination.To develop students' mathematical thinking effectively,it is not wise to find a way which is divorced from the constraints.Instead,we should find a way which is not only combined with the examination requirements,but also good for the training of students' mathematical thinking.
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Researchers have identified the tendency of students to think superficially and abstain from sense-making when confronted with arithmetic word problems (Verschaffel, Greer & De Corte, 2000). Research has found that the nature of word problems used in mathematics classrooms is important for developing students’ realistic reasoning. Exposure to situationally rich problems (which resemble authentic quantitative problems people may encounter in real life) is considered essential for triggering students’ sense-making in problem solving. Our analysis focused on the new 5th-grade elementary mathematics textbook published by the Pedagogic Institute of Greece following a major mathematics educational reform that took place in 2003. This reform meant to promote inter alia critical reasoning in problem solving (Pedagogic Institute, 2003). In particular, we examined whether the word problems in the new textbook are close to authentic out-of-school quantitative problems and how they compare with the ones contained in the old textbook. For our analysis we used a classification framework developed to measure the degree of simulation at which a number of aspects of reality are represented in word problems (Palm & Burman, 2004; Depaepe, De Corte, & Verschaffel, 2009). Our comparative analysis showed some changes in the representation of different aspects, as well as persistent shortcomings.
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The objective of this article is to describe the phenomenology of analytical thinking with open method students based on the assessment of 21st-century mathematics learning, it was found that the phenomenology of analytical thinking with the open method of students was based on the assessment of learning. Know mathematics in the 21st century, both of which are 4 steps of the Open Approach in math class. It is characterized by a phenomenology, ideology, mentioned as an independent idea of the subject to be studied. To describe the meaning that is built into the conscious mind, the student must not have prejudice. And there is no bias in the subject studied by eliminating one's opinion from what we are studying (bracketing) the focus on purpose. The intentionality and essence of a person's perception are believed that human beings can understand what is experienced through it. In summary, by linking math ideas for this step, teachers will allow students to display individual work or group work on the front board for students to join the class. Moreover, if possible, teachers are advised to show all student work. Although there may be jobs with similar or similar concepts. The work is not complete. Or works with errors Teachers should therefore be able to positively express the student's works or ideas, and then gradually. Correct incorrect ideas from exchanging and suggesting from fellow students.
CLARITY
Intentionality
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The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to problem situations. Above all, the use of appropriate language is the key to making mathematics intelligible. In a very real sense, mathematics is a language. Proficiency in this language can be acquired only by long and carefully supervised experience in using it in situations involving argument and proof. Mathematics is essentially a structured hierarchy of proposition forged by logic on a postulation base. However, nowadays, the teaching of mathematics is more on focusing the mathematical procedures. Students learn variety of problem-solving in mathematics and then on its application. In addition, the teaching of mathematics is moving towards the use of mathematics in the real world. This method is said to motivate students to learn mathematics and enable them to transfer this knowledge in their daily live and future career. There are beliefs that due to the current over-emphasis on problem-solving and applications, students who enjoy working the problems in high school math, and hence decide that they like mathematics and want to major in it, find that the nature of the subject changes abruptly when they encounter the proof courses. They are bewildered and dismayed. Their previous problem-solving courses did not prepare them for this abrupt changed. Is argument and proof in the applications-problem centered domain of school mathematics being postponed, suppressed and downgraded? Are we sacrificing the essence of mathematics in order to motivate students to learn and appreciate mathematics? In this paper, the authors will discuss on this issue.
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Argument (complex analysis)
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This study examines the relationship between the grasp of consciousness of the reasoning process in Grades 5 and 8 pupils from a public and a private school, and their performance in mathematical problems of Cartesian product. Forty-two participants aged from 10 to 16 solved four problems in writing and explained their solution procedures by answering the question: “How did I think to solve this problem?”. The qualitative analysis identified three response categories as indicators of the participants’ grasp of consciousness regarding their ways of reasoning involved in finding the solutions, which can be explained by the reflecting abstractions model. The statistical analysis showed those categories as associated with the performance: progressively more refined justifications came along with mathematically correct solutions to the problems. Differences in performance and the use of justifications for the solutions by participants of both types of school corroborate that result. A teaching process directed towards students’ reflection and comprehension regarding specific schemes and conceptual mathematical relations may be at the root of these differences. Thus, teachers’ interventions that encourage students to think about their own thinking are recommended.
Cartesian product
Thinking processes
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